{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning-to-rank using the WARP loss\n",
    "\n",
    "LightFM is probably the only recommender package implementing the WARP (Weighted Approximate-Rank Pairwise) loss for implicit feedback learning-to-rank. Generally, it perfoms better than the more popular BPR (Bayesian Personalised Ranking) loss --- often by a large margin.\n",
    "\n",
    "It was originally applied to image annotations in the Weston et al. [WSABIE paper](http://www.thespermwhale.com/jaseweston/papers/wsabie-ijcai.pdf), but has been extended to apply to recommendation settings in the [2013 k-order statistic loss paper](http://www.ee.columbia.edu/~ronw/pubs/recsys2013-kaos.pdf) in the form of the k-OS WARP loss, also implemented in LightFM.\n",
    "\n",
    "Like the BPR model, WARP deals with (user, positive item, negative item) triplets. Unlike BPR, the negative items in the triplet are not chosen by random sampling: they are chosen from among those negatie items which would violate the desired item ranking given the state of the model. This approximates a form of active learning where the model selects those triplets that it cannot currently rank correctly.\n",
    "\n",
    "This procedure yields roughly the following algorithm:\n",
    "\n",
    "1. For a given (user, positive item pair), sample a negative item at random from all the remaining items. Compute predictions for both items; if the negative item's prediction exceeds that of the positive item plus a margin, perform a gradient update to rank the positive item higher and the negative item lower. If there is no rank violation, continue sampling negative items until a violation is found.\n",
    "2. If you found a violating negative example at the first try, make a large gradient update: this indicates that a lot of negative items are ranked higher than positives items given the current state of the model, and the model must be updated by a large amount. If it took a lot of sampling to find a violating example, perform a small update: the model is likely close to the optimum and should be updated at a low rate.\n",
    "\n",
    "While this is fairly hand-wavy, it should give the correct intuition. For more details, read the paper itself or a more in-depth blog post [here](https://building-babylon.net/2016/03/18/warp-loss-for-implicit-feedback-recommendation/). A similar approach for BPR is described in Rendle's 2014 [WSDM 2014 paper](http://webia.lip6.fr/~gallinar/gallinari/uploads/Teaching/WSDM2014-rendle.pdf).\n",
    "\n",
    "Having covered the theory, the rest of this example looks at the practical implications of using WARP in LightFM.\n",
    "\n",
    "## Preliminaries\n",
    "Let's first get the data. We'll use the MovieLens 100K dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import time\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from lightfm import LightFM\n",
    "from lightfm.datasets import fetch_movielens\n",
    "from lightfm.evaluation import auc_score\n",
    "\n",
    "movielens = fetch_movielens()\n",
    "\n",
    "train, test = movielens['train'], movielens['test']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accuracy\n",
    "The first interesting experiment is to compare the accuracy between the WARP and BPR losses. Let's fit two models with equivalent hyperparameters and compare their accuracy across epochs. Whilst we're fitting them, let's also measure how much time each epoch takes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "alpha = 1e-05\n",
    "epochs = 70\n",
    "num_components = 32\n",
    "\n",
    "warp_model = LightFM(no_components=num_components,\n",
    "                    loss='warp',\n",
    "                    learning_schedule='adagrad',\n",
    "                    max_sampled=100,\n",
    "                    user_alpha=alpha,\n",
    "                    item_alpha=alpha)\n",
    "\n",
    "bpr_model = LightFM(no_components=num_components,\n",
    "                    loss='bpr',\n",
    "                    learning_schedule='adagrad',\n",
    "                    user_alpha=alpha,\n",
    "                    item_alpha=alpha)\n",
    "\n",
    "warp_duration = []\n",
    "bpr_duration = []\n",
    "warp_auc = []\n",
    "bpr_auc = []\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    start = time.time()\n",
    "    warp_model.fit_partial(train, epochs=1)\n",
    "    warp_duration.append(time.time() - start)\n",
    "    warp_auc.append(auc_score(warp_model, test, train_interactions=train).mean())\n",
    "    \n",
    "for epoch in range(epochs):\n",
    "    start = time.time()\n",
    "    bpr_model.fit_partial(train, epochs=1)\n",
    "    bpr_duration.append(time.time() - start)\n",
    "    bpr_auc.append(auc_score(bpr_model, test, train_interactions=train).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the results immediately reveals that WARP produces superior results: a smarter way of selecting negative examples leads to higher quality rankings. Test accuracy decreases after the first 10 epochs, suggesting WARP starts overfitting and would benefit from regularization or early stopping."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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I4O677+aDDz7g1Vdfbce72d8ugIkTJ7a4fcKECaSnp4cdovr444+zbds2Ro0axYMPPsjv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\nQUJERESipiAhIiIiUft/jSXP5tT9l4AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb32a1e81d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(epochs)\n",
    "plt.plot(x, np.array(warp_auc))\n",
    "plt.plot(x, np.array(bpr_auc))\n",
    "plt.legend(['WARP AUC', 'BPR AUC'], loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting speed\n",
    "\n",
    "What about model fitting speed?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AMMGBOicBmGSkPURUNNiasWFSqhRQr17OhMuoKAkw2rUDKlSojfj4eJw7dy7H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\nTdM0zWo6kdA0TdM0zWr/D25KUpgBVtvSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb3296a4810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(epochs)\n",
    "plt.plot(x, np.array(warp_duration))\n",
    "plt.plot(x, np.array(bpr_duration))\n",
    "plt.legend(['WARP duration', 'BPR duration'], loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "WARP is slower than BPR for all epochs. Interestingly, however, it gets slower with additional epochs; every subsequent epoch takes more time. This is because of WARP's adaptive samling of negatives: the closer the model fits the training data, the more times it needs to sample in order to find rank-violating examples, leading to longer fitting times.\n",
    "\n",
    "For this reason, LightFM exposes the `max_sampled` hyperparameter that limits the number of attemps WARP will carry out to find a negative. Setting it to a low value and repeating the run shows that the run time actually decreases with every epoch: this is because no updates happen when a violating example cannot be found in the specified number of attempts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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539u0AerW9e2JEBERRbuUlBSkpOT/cp2ZmYnk5OSAXcOvGgljzBkAGQCuto6J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\nXWtxmjbVmVKBHN5wLrR01rO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1A2nvXuD663W5e7uWLNHgoX9/HV665hotuD12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\njMmNHQljjDHG5Oa/Q47b80hNiJ8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb32997ce90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4ChgL9AceBJ40s2MSypwE3A98FTgTaAs8b2YdU61fQ2bNgnPO0U26REREWko6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\niIikTUFCRERE0qYgISIiImn7/wHeyxZlFRJvFgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb32a4e74d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "warp_model = LightFM(no_components=num_components,\n",
    "                     max_sampled=3,\n",
    "                    loss='warp',\n",
    "                    learning_schedule='adagrad',\n",
    "                    user_alpha=alpha,\n",
    "                    item_alpha=alpha)\n",
    "\n",
    "warp_duration = []\n",
    "warp_auc = []\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    start = time.time()\n",
    "    warp_model.fit_partial(train, epochs=1)\n",
    "    warp_duration.append(time.time() - start)\n",
    "    warp_auc.append(auc_score(warp_model, test, train_interactions=train).mean())\n",
    "\n",
    "x = np.arange(epochs)\n",
    "plt.plot(x, np.array(warp_duration))\n",
    "plt.legend(['WARP duration'], loc='upper right')\n",
    "plt.title('Duration')\n",
    "plt.show()\n",
    "\n",
    "x = np.arange(epochs)\n",
    "plt.plot(x, np.array(warp_auc))\n",
    "plt.legend(['WARP AUC'], loc='upper right')\n",
    "plt.title('AUC')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
